## Monday, February 23, 2015

### Unizor - Probability - Easy Problems 2

Problem A

Assume that the probability of snowing on December 25th is 0.4.

Assume also that the climate is not changing during the next 10 years, so this probability remains constant throughout the years.

What is the probability of snowing on exactly 3 different December 25th dates out of the next 10 years?

Problem B

A discrete random variable takes values

1/2, 1/4, 1/8,...,1/2n,1/2n+1,...

with probabilities, correspondingly,

1/2, 1/4, 1/8,...,1/2n,1/2n+1,....

As you see, there are infinite number of values it can take and, correspondingly, infinite number of probabilities.

(a) Check that the sum of all probabilities equals to 1.

(b) Determine a probability for our random variable to be between 1/2^m and 1/2^n (inclusive, where m is smaller than n).

(c) Calculate the expected value of this random variable.

Problem C

A person is trying to call a friend, but he forgot the last digit of the friend's number. So, he tries to randomly choose the last digit and, if it's a wrong number, tries another digit at the end. Obviously, it requires no more than 10 attempts to succeed.

What is the probability of succeeding no later than on the Nth try, assuming he does not repeat dialing the wrong numbers that he already dialed before?

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